COMPASSES

, or Pair of Compasses, a mathematical instrument for describing circles, measuring and dividing lines, or figures, &c.

The common compasses consist of two sharp-pointed branches or legs of iron, steel, brass, or other metal, joined together at the top by a rivet, about which they move as on a centre. Those compasses are of the best fort in which the pin or axle, on which the joint turns, is made of steel, and also half the joint itself, as the opposite metals wear more equally: the points should also be made of hard steel, well polished; and the joint should open and shut with a smooth, easy, and uniform motion. In some compasses, the points are both fixed; but in others, one is made to take out occasionally, and a drawing-pen, or pencil, put in its place.

There are in use compasses of various kinds and contrivances, adapted to the various purposes they are intended for; as,

Compasses of three Legs, or Triangular Compasses; the construction of which is like that of the common compasses, with the addition of a third leg or point, | which has a motion every way. Their use is to take three points at once, and so to form triangles, and lay down three positions of a map to be copied at once.

Beam Compasses consist of a long straight beam or bar, carrying two brass cursors; one of these being fixed at one end, the other sliding along the beam, with a screw to fasten it on occasionally. To the cursors may be screwed points of any kind, whether steel, pencils, or the like. To the sixed cursor is sometimes applied an adjusting or micrometer screw, by which an extent is obtained to very great nicety. The beam compasses are used to draw large circles, to take great extents, or the like.

Bow Compasses, or Bows, are a small sort of compasses, that shut up in a hoop, which serves for a handle. Their use is to describe arcs or circumserences with a very small radius.

Caliber Compasses. See Caliber.

Clockmakers Compasses are jointed like the common compasses, with a quadrant or bow, like the spring compasses; only of different use, serving here to keep the instrument firm at any opening. They are made very strong, with the points of their legs of well-tempered steel, as being used to draw or cut lines in pasteboard, or copper, &c.

Cylindrical and Spherical Compasses, consist of four branches, joined in a centre, two of them being circular and two flat, a little bent at the ends. The use of them is to take the diameter, thickness, or caliber of round or cylindrical bodies; as cannons, balls, pipes, &c.

There are also spherical compasses, differing in nothing from the common ones, but that their legs are arched; serving to take the diameters of round bodies.

There is also another sort of compasses lately invented, for measuring the diameter of round bodies, as balls, &c, which consist of two slat pieces of metal set at right angles on a straight bar or beam of the same; the one piece being fixed, and the other sliding along it, so far as just to receive the round body between them; and then its diameter, or distance between the two pieces, is shewn by the divisions marked on the beam.

Elliptical Compasses, are used to draw ellipses or ovals of any kind. The instrument consists of a beam AB (Plate vi. fig. 6.) about a foot long, bearing three cursors; to one of which may be screwed points of any kind; and to the bottom of the other two are rivetted two sliding dove-tails, adjusted in grooves made in the cross branches of the beam. The dove-tails having a motion every way, by turning about the long branch, they go backward and forward along the cross; so that when the beam has gone half way round, one of these will have moved the whole length of one of the branches; and when the beam has gone quite round, the same dove-tail has gone back the whole length of the branch. Understand the same of the other dovetail.

Note, the distance between the two sliding dovetails, is the distance between the two foci of the ellipse; so that by changing that distance, the ellipse will be rounder or flatter. Under the ends of the branches of the cross, are placed four steel points to keep it fast.

The use of this compass is easy: by turning round the long branch, the pen, pencil, or other points will draw the ellipse required.

Its figure shews both its use and construction.

German Compasses have their legs a little bent outwards, near the top; so that when shut, the points only meet.

Hair Compasses are so contrived within side by a small adjusting screw to one of the legs, as to take an extent to a hair's breadth, or great exactness.

Proportional Compasses are those whose joint lies, not at the end of the legs, but between the points terminating each leg. These are either simple, or compound. In the former sort the centre, or place of the joint is fixed; so that one pair of these serves only for one proportion.

Compound Proportional Compasses have the joint or centre moveable. They consist of two parts or sides of brass, which lie upon each other so nicely as to seem but one when they are shut. These sides easily open, and move about the centre, which is itself moveable in a hollow canal cut through the greatest part of their length. To this centre on each side is sixed a sliding piece, of a small length, with a sine line drawn on it serving as an index, to be set against other lines or divisions placed upon the compasses on both sides. These lines are, 1, A line of lines; 2, a line of supersicies, areas, or planes, the numbers on which answer to the squares of those on the line of lines; 3, a line of solids, the numbers on which answer to the cubes of those on the line of lines; 4, a line of circles, or rather of polygons to be inscribed in circles. These lines are all unequally divided, the first three from 1 to 20, and the last from 6 to 20. The use of the first is to divide a line into any number of equal parts; by the 2d and 3d are found the sides of like planes or solids in any given proportion; and by the 4th, circles are divided into any number of equal parts, or any polygons inscribed in them. See Plate vi. fig. 7.

Spring Compasses, or Dividers, are made of hardened steel, with an arched head, which by its spring opens the legs; the opening being directed by a circular screw fastened to one of the legs, let through the other, and worked with a nut.

Trisecting Compasses, for the trisecting of angles geometrically, for which purpose they were invented by M. Tarragon.

The instrument consists of two central rules, and an arch of a circle of 120 degrees, immoveable, with its radius: the radius is fastened with one of the central rules, like the two legs of a sector, that the central rule may be carried through all the points of the circumference of the arch. The radius and rule should be as thin as possible; and the rule fastened to the radius should be hammered cold, to be more elastic; and the breadth of the other central rule must be triple the breadth of the radius: in this rule also is a groove, with a dove-tail fastened on it, for its motion; there must also be a hole in the centre of each rule.

Turn-up Compasses, a late contrivance to save the trouble of changing the points: the body is like the common compasses; and towards the bottom of the legs without side, are added two other points, besides the usual ones; the one carrying a drawing pen point, and | the other a port-crayon; both being adjusted to turn up, to be used or not, as occasion may require.

COMPLEMENT in general, is what is wanting, or necessary, to complete some certain quantity or thing. As, the

Complement of an arch or angle, as of 90° or a quadrant, is what any given arch or angle wants of it; so the complement of 50° is 40°, and the complement of 100 degrees is —10°, a negative quantity.—The complement to 180° is usually called the supplement, to distinguish it from the complement to 90°, properly so called.—The sine of the complement of an arc, is contracted into the word cosine; the tangent of the complement, into cotangent; &c.

Arithmetical Complement, is what a number or logarithm wants of unity or 1 with some number of ciphers. It is best found, by beginning at the left-hand side, and subtracting every figure from 9, except the last, or right-hand figure, which must be subtracted from 10. So, the arithmetical comp. of the log. 9.5329714, by subtracting from 9's, &c, is 0.4670286.

The arithmetical complements are much used in operations by logarithms, to change subtractions into additions, which are more conveniently performed, especially when there are more than one of them in the operation.

, in Astronomy, is used for the distance of a star from the zenith; or the arc contained between the zenith and the place of a star which is above the horizon. It is the same as the complement of the altitude, or co-altitude, or the zenith distance.

Complement of the Course, in Navigation, is the quantity which the course wants of 90°, or 8 points, viz, a quarter of the compass.

Complement of the Curtain, in Fortisication, is that part of the anterior side of the curtain, which makes the demigorge.

Complement of the Line of Defence, is the remainder of that line, after the angle of the flank is taken away.

Complements of a Parallelogram, or in a Parallelogram, are the two lesser parallelograms, made by drawing two right lines parallel to each side of the given parallelo- gram, through the same point in the diagonal. So P and Q are the complements in the parallelogram ABCD.

In every case, these complements are always equal, viz, the parallelogram P = Q.

Complement of Life, a term much used, in the doctrine of Life Annuities, by De Moivre, and, according to him, it denotes the number of years which a given life wants of 86, this being the age which he considered as the utmost probable extent of life. So 56 is the complement of 30, and 30 is the complement of 56.

That author supposed an equal annual decrement of lise through all its stages, till the age of 86. Thus, if there be 56 persons living at 30 years of age, it is supposed that one will die every year, till they be all dead in 56 years. This hypothesis in many cases is very near the truth; and it agrees so nearly with Halley's table, formed from his observations of the mortuary bills of Breslaw, that the value of lives deduced either from the hypothesis, or the table, need not be distinguished; hence it very much eases the labour of calculating them. See Life Annuities, also De Moivre's Treatise on Annuities, pa. 83, and Price on Reversionary Payments, pa. 2.

COMPOSITE Number, is one that is compounded of, or made up by the multiplication of two other numbers, greater than 1, or which can be measured by some other number greater than 1. As 12, which is composed, or compounded of 2 and 6, or 3 and 4, viz by multiplying together 2 and 6, or 3 and 4, both products making the same number 12; which therefore is a composite number.

Composites are opposed to prime numbers, or primes, which cannot be exactly measured by any other number, and cannot be produced by multiplying together two other factors.

Composite Numbers between themselves, are the same with commensurable numbers, or such as have a common measure or factor; as 15 and 12, which have the common term 3.

The doctrine of Prime and Composite numbers is pretty fully treated in the 7th and 8th books of Euclid's Elements.

Composite Order, in Architecture, is the last of the five orders of columns; and is so called because its capital is composed out of those of the other orders. Thus, it borrows a quarter-round from the Tuscan and Doric; a double row of leaves from the Corinthian; and volutes from the Ionic. Its cornice has single modillions, or dentils; and its column is 10 diameters in height.

This order is also called the Roman order, and Italic order, as having been invented by the Romans, like as the other orders are denominated from the people among whom they had their rise.